Periodic Cosmic String Formation and Dynamics

We study string formation and dynamics in a scalar field theory with a global $U(1)$ symmetry. If a scalar field $\Phi$ is initially displaced from the minimum of a wine-bottle potential, even if uniformly over large spatial patches, small spatial perturbations to $\Phi$ grow via parametric resonance as $\Phi$ oscillates; this occurs for a wide range of initial $U(1)$ charge densities. The growth of perturbations leads to the formation of spatially coherent, temporally stable "counter-rotating regions" (CRR): spatially connected regions exhibiting $\Phi$ evolution with large, opposite-sign rotation speeds in field space which persist over long durations. These CRR are separated by domain boundaries that have a large field gradient and zero rotational speed in field space. String or vortex topological defects form, are confined to, and then annihilate periodically on these boundaries. We demonstrate these periodic dynamics with numerical simulations in both 2+1 and 3+1 dimensions, in both Minkowski spacetime and in a radiation-dominated FLRW universe, and we explain some features of the evolution (semi-)analytically. At late times in an expanding universe, when $\Phi$ approaches the potential minimum, the CRR and vortices dissipate into scalar radiation. Phenomenologically, periodic bursts of string formation and annihilation can lead to periodic bursts of gravitational-wave production. For small initial $U(1)$ charge density, these gravitational-wave bursts can be synchronized across the whole Universe. Owing to their periodic nature, they could give rise to a gravitational-wave frequency spectrum consisting of a forest of peaks. These periodic scalar field dynamics also occur with large, untuned initial $U(1)$ charge density; they may thus have implications for models that depend on a coherent field rotation, such as kination and the axion kinetic-misalignment mechanism. [abridged]